Recent advances and challenges in deterministic global optimization
Wednesday, April 9, 2008 - 11:15am - 12:15pm
In this presentation, we will provide an overview of the research progress in global optimization. The focus will be on important contributions during the last five years, and will provide a perspective for future research opportunities. The overview will cover the areas of (a) twice continuously differentiable constrained nonlinear optimization, and (b) mixed-integer nonlinear optimization models. Subsequently, we will present our recent fundamental advances in (i) convex envelope results for multi-linear functions, (ii) a piecewise quadratic convex underestimator for twice continuously differentiable functions, (iii) the generalized alpha-BB framework, (iv) our recently improved convex underestimation techniques for univariate and multivariate functions, and (v) generalized pooling problems. Computational studies will illustrate the potential of these advances.